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trezor-firmware/ecdsa.c
Jochen Hoenicke 9dfc6a4477
introduce confidential macro, mark confidential items
2017-08-16 13:38:49 +02:00

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/**
* Copyright (c) 2013-2014 Tomas Dzetkulic
* Copyright (c) 2013-2014 Pavol Rusnak
* Copyright (c) 2015 Jochen Hoenicke
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included
* in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES
* OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
* OTHER DEALINGS IN THE SOFTWARE.
*/
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include "address.h"
#include "bignum.h"
#include "rand.h"
#include "sha2.h"
#include "ripemd160.h"
#include "hmac.h"
#include "ecdsa.h"
#include "base58.h"
#include "macros.h"
#include "secp256k1.h"
#include "rfc6979.h"
// Set cp2 = cp1
void point_copy(const curve_point *cp1, curve_point *cp2)
{
*cp2 = *cp1;
}
// cp2 = cp1 + cp2
void point_add(const ecdsa_curve *curve, const curve_point *cp1, curve_point *cp2)
{
bignum256 lambda, inv, xr, yr;
if (point_is_infinity(cp1)) {
return;
}
if (point_is_infinity(cp2)) {
point_copy(cp1, cp2);
return;
}
if (point_is_equal(cp1, cp2)) {
point_double(curve, cp2);
return;
}
if (point_is_negative_of(cp1, cp2)) {
point_set_infinity(cp2);
return;
}
bn_subtractmod(&(cp2->x), &(cp1->x), &inv, &curve->prime);
bn_inverse(&inv, &curve->prime);
bn_subtractmod(&(cp2->y), &(cp1->y), &lambda, &curve->prime);
bn_multiply(&inv, &lambda, &curve->prime);
// xr = lambda^2 - x1 - x2
xr = lambda;
bn_multiply(&xr, &xr, &curve->prime);
yr = cp1->x;
bn_addmod(&yr, &(cp2->x), &curve->prime);
bn_subtractmod(&xr, &yr, &xr, &curve->prime);
bn_fast_mod(&xr, &curve->prime);
bn_mod(&xr, &curve->prime);
// yr = lambda (x1 - xr) - y1
bn_subtractmod(&(cp1->x), &xr, &yr, &curve->prime);
bn_multiply(&lambda, &yr, &curve->prime);
bn_subtractmod(&yr, &(cp1->y), &yr, &curve->prime);
bn_fast_mod(&yr, &curve->prime);
bn_mod(&yr, &curve->prime);
cp2->x = xr;
cp2->y = yr;
}
// cp = cp + cp
void point_double(const ecdsa_curve *curve, curve_point *cp)
{
bignum256 lambda, xr, yr;
if (point_is_infinity(cp)) {
return;
}
if (bn_is_zero(&(cp->y))) {
point_set_infinity(cp);
return;
}
// lambda = (3 x^2 + a) / (2 y)
lambda = cp->y;
bn_mult_k(&lambda, 2, &curve->prime);
bn_inverse(&lambda, &curve->prime);
xr = cp->x;
bn_multiply(&xr, &xr, &curve->prime);
bn_mult_k(&xr, 3, &curve->prime);
bn_subi(&xr, -curve->a, &curve->prime);
bn_multiply(&xr, &lambda, &curve->prime);
// xr = lambda^2 - 2*x
xr = lambda;
bn_multiply(&xr, &xr, &curve->prime);
yr = cp->x;
bn_lshift(&yr);
bn_subtractmod(&xr, &yr, &xr, &curve->prime);
bn_fast_mod(&xr, &curve->prime);
bn_mod(&xr, &curve->prime);
// yr = lambda (x - xr) - y
bn_subtractmod(&(cp->x), &xr, &yr, &curve->prime);
bn_multiply(&lambda, &yr, &curve->prime);
bn_subtractmod(&yr, &(cp->y), &yr, &curve->prime);
bn_fast_mod(&yr, &curve->prime);
bn_mod(&yr, &curve->prime);
cp->x = xr;
cp->y = yr;
}
// set point to internal representation of point at infinity
void point_set_infinity(curve_point *p)
{
bn_zero(&(p->x));
bn_zero(&(p->y));
}
// return true iff p represent point at infinity
// both coords are zero in internal representation
int point_is_infinity(const curve_point *p)
{
return bn_is_zero(&(p->x)) && bn_is_zero(&(p->y));
}
// return true iff both points are equal
int point_is_equal(const curve_point *p, const curve_point *q)
{
return bn_is_equal(&(p->x), &(q->x)) && bn_is_equal(&(p->y), &(q->y));
}
// returns true iff p == -q
// expects p and q be valid points on curve other than point at infinity
int point_is_negative_of(const curve_point *p, const curve_point *q)
{
// if P == (x, y), then -P would be (x, -y) on this curve
if (!bn_is_equal(&(p->x), &(q->x))) {
return 0;
}
// we shouldn't hit this for a valid point
if (bn_is_zero(&(p->y))) {
return 0;
}
return !bn_is_equal(&(p->y), &(q->y));
}
// Negate a (modulo prime) if cond is 0xffffffff, keep it if cond is 0.
// The timing of this function does not depend on cond.
void conditional_negate(uint32_t cond, bignum256 *a, const bignum256 *prime)
{
int j;
uint32_t tmp = 1;
assert(a->val[8] < 0x20000);
for (j = 0; j < 8; j++) {
tmp += 0x3fffffff + 2*prime->val[j] - a->val[j];
a->val[j] = ((tmp & 0x3fffffff) & cond) | (a->val[j] & ~cond);
tmp >>= 30;
}
tmp += 0x3fffffff + 2*prime->val[j] - a->val[j];
a->val[j] = ((tmp & 0x3fffffff) & cond) | (a->val[j] & ~cond);
assert(a->val[8] < 0x20000);
}
typedef struct jacobian_curve_point {
bignum256 x, y, z;
} jacobian_curve_point;
// generate random K for signing/side-channel noise
static void generate_k_random(bignum256 *k, const bignum256 *prime) {
do {
int i;
for (i = 0; i < 8; i++) {
k->val[i] = random32() & 0x3FFFFFFF;
}
k->val[8] = random32() & 0xFFFF;
// check that k is in range and not zero.
} while (bn_is_zero(k) || !bn_is_less(k, prime));
}
void curve_to_jacobian(const curve_point *p, jacobian_curve_point *jp, const bignum256 *prime) {
// randomize z coordinate
generate_k_random(&jp->z, prime);
jp->x = jp->z;
bn_multiply(&jp->z, &jp->x, prime);
// x = z^2
jp->y = jp->x;
bn_multiply(&jp->z, &jp->y, prime);
// y = z^3
bn_multiply(&p->x, &jp->x, prime);
bn_multiply(&p->y, &jp->y, prime);
}
void jacobian_to_curve(const jacobian_curve_point *jp, curve_point *p, const bignum256 *prime) {
p->y = jp->z;
bn_inverse(&p->y, prime);
// p->y = z^-1
p->x = p->y;
bn_multiply(&p->x, &p->x, prime);
// p->x = z^-2
bn_multiply(&p->x, &p->y, prime);
// p->y = z^-3
bn_multiply(&jp->x, &p->x, prime);
// p->x = jp->x * z^-2
bn_multiply(&jp->y, &p->y, prime);
// p->y = jp->y * z^-3
bn_mod(&p->x, prime);
bn_mod(&p->y, prime);
}
void point_jacobian_add(const curve_point *p1, jacobian_curve_point *p2, const ecdsa_curve *curve) {
bignum256 r, h, r2;
bignum256 hcby, hsqx;
bignum256 xz, yz, az;
int is_doubling;
const bignum256 *prime = &curve->prime;
int a = curve->a;
assert (-3 <= a && a <= 0);
/* First we bring p1 to the same denominator:
* x1' := x1 * z2^2
* y1' := y1 * z2^3
*/
/*
* lambda = ((y1' - y2)/z2^3) / ((x1' - x2)/z2^2)
* = (y1' - y2) / (x1' - x2) z2
* x3/z3^2 = lambda^2 - (x1' + x2)/z2^2
* y3/z3^3 = 1/2 lambda * (2x3/z3^2 - (x1' + x2)/z2^2) + (y1'+y2)/z2^3
*
* For the special case x1=x2, y1=y2 (doubling) we have
* lambda = 3/2 ((x2/z2^2)^2 + a) / (y2/z2^3)
* = 3/2 (x2^2 + a*z2^4) / y2*z2)
*
* to get rid of fraction we write lambda as
* lambda = r / (h*z2)
* with r = is_doubling ? 3/2 x2^2 + az2^4 : (y1 - y2)
* h = is_doubling ? y1+y2 : (x1 - x2)
*
* With z3 = h*z2 (the denominator of lambda)
* we get x3 = lambda^2*z3^2 - (x1' + x2)/z2^2*z3^2
* = r^2 - h^2 * (x1' + x2)
* and y3 = 1/2 r * (2x3 - h^2*(x1' + x2)) + h^3*(y1' + y2)
*/
/* h = x1 - x2
* r = y1 - y2
* x3 = r^2 - h^3 - 2*h^2*x2
* y3 = r*(h^2*x2 - x3) - h^3*y2
* z3 = h*z2
*/
xz = p2->z;
bn_multiply(&xz, &xz, prime); // xz = z2^2
yz = p2->z;
bn_multiply(&xz, &yz, prime); // yz = z2^3
if (a != 0) {
az = xz;
bn_multiply(&az, &az, prime); // az = z2^4
bn_mult_k(&az, -a, prime); // az = -az2^4
}
bn_multiply(&p1->x, &xz, prime); // xz = x1' = x1*z2^2;
h = xz;
bn_subtractmod(&h, &p2->x, &h, prime);
bn_fast_mod(&h, prime);
// h = x1' - x2;
bn_add(&xz, &p2->x);
// xz = x1' + x2
// check for h == 0 % prime. Note that h never normalizes to
// zero, since h = x1' + 2*prime - x2 > 0 and a positive
// multiple of prime is always normalized to prime by
// bn_fast_mod.
is_doubling = bn_is_equal(&h, prime);
bn_multiply(&p1->y, &yz, prime); // yz = y1' = y1*z2^3;
bn_subtractmod(&yz, &p2->y, &r, prime);
// r = y1' - y2;
bn_add(&yz, &p2->y);
// yz = y1' + y2
r2 = p2->x;
bn_multiply(&r2, &r2, prime);
bn_mult_k(&r2, 3, prime);
if (a != 0) {
// subtract -a z2^4, i.e, add a z2^4
bn_subtractmod(&r2, &az, &r2, prime);
}
bn_cmov(&r, is_doubling, &r2, &r);
bn_cmov(&h, is_doubling, &yz, &h);
// hsqx = h^2
hsqx = h;
bn_multiply(&hsqx, &hsqx, prime);
// hcby = h^3
hcby = h;
bn_multiply(&hsqx, &hcby, prime);
// hsqx = h^2 * (x1 + x2)
bn_multiply(&xz, &hsqx, prime);
// hcby = h^3 * (y1 + y2)
bn_multiply(&yz, &hcby, prime);
// z3 = h*z2
bn_multiply(&h, &p2->z, prime);
// x3 = r^2 - h^2 (x1 + x2)
p2->x = r;
bn_multiply(&p2->x, &p2->x, prime);
bn_subtractmod(&p2->x, &hsqx, &p2->x, prime);
bn_fast_mod(&p2->x, prime);
// y3 = 1/2 (r*(h^2 (x1 + x2) - 2x3) - h^3 (y1 + y2))
bn_subtractmod(&hsqx, &p2->x, &p2->y, prime);
bn_subtractmod(&p2->y, &p2->x, &p2->y, prime);
bn_multiply(&r, &p2->y, prime);
bn_subtractmod(&p2->y, &hcby, &p2->y, prime);
bn_mult_half(&p2->y, prime);
bn_fast_mod(&p2->y, prime);
}
void point_jacobian_double(jacobian_curve_point *p, const ecdsa_curve *curve) {
bignum256 az4, m, msq, ysq, xysq;
const bignum256 *prime = &curve->prime;
assert (-3 <= curve->a && curve->a <= 0);
/* usual algorithm:
*
* lambda = (3((x/z^2)^2 + a) / 2y/z^3) = (3x^2 + az^4)/2yz
* x3/z3^2 = lambda^2 - 2x/z^2
* y3/z3^3 = lambda * (x/z^2 - x3/z3^2) - y/z^3
*
* to get rid of fraction we set
* m = (3 x^2 + az^4) / 2
* Hence,
* lambda = m / yz = m / z3
*
* With z3 = yz (the denominator of lambda)
* we get x3 = lambda^2*z3^2 - 2*x/z^2*z3^2
* = m^2 - 2*xy^2
* and y3 = (lambda * (x/z^2 - x3/z3^2) - y/z^3) * z3^3
* = m * (xy^2 - x3) - y^4
*/
/* m = (3*x^2 + a z^4) / 2
* x3 = m^2 - 2*xy^2
* y3 = m*(xy^2 - x3) - 8y^4
* z3 = y*z
*/
m = p->x;
bn_multiply(&m, &m, prime);
bn_mult_k(&m, 3, prime);
az4 = p->z;
bn_multiply(&az4, &az4, prime);
bn_multiply(&az4, &az4, prime);
bn_mult_k(&az4, -curve->a, prime);
bn_subtractmod(&m, &az4, &m, prime);
bn_mult_half(&m, prime);
// msq = m^2
msq = m;
bn_multiply(&msq, &msq, prime);
// ysq = y^2
ysq = p->y;
bn_multiply(&ysq, &ysq, prime);
// xysq = xy^2
xysq = p->x;
bn_multiply(&ysq, &xysq, prime);
// z3 = yz
bn_multiply(&p->y, &p->z, prime);
// x3 = m^2 - 2*xy^2
p->x = xysq;
bn_lshift(&p->x);
bn_fast_mod(&p->x, prime);
bn_subtractmod(&msq, &p->x, &p->x, prime);
bn_fast_mod(&p->x, prime);
// y3 = m*(xy^2 - x3) - y^4
bn_subtractmod(&xysq, &p->x, &p->y, prime);
bn_multiply(&m, &p->y, prime);
bn_multiply(&ysq, &ysq, prime);
bn_subtractmod(&p->y, &ysq, &p->y, prime);
bn_fast_mod(&p->y, prime);
}
// res = k * p
void point_multiply(const ecdsa_curve *curve, const bignum256 *k, const curve_point *p, curve_point *res)
{
// this algorithm is loosely based on
// Katsuyuki Okeya and Tsuyoshi Takagi, The Width-w NAF Method Provides
// Small Memory and Fast Elliptic Scalar Multiplications Secure against
// Side Channel Attacks.
assert (bn_is_less(k, &curve->order));
int i, j;
static CONFIDENTIAL bignum256 a;
uint32_t *aptr;
uint32_t abits;
int ashift;
uint32_t is_even = (k->val[0] & 1) - 1;
uint32_t bits, sign, nsign;
static CONFIDENTIAL jacobian_curve_point jres;
curve_point pmult[8];
const bignum256 *prime = &curve->prime;
// is_even = 0xffffffff if k is even, 0 otherwise.
// add 2^256.
// make number odd: subtract curve->order if even
uint32_t tmp = 1;
uint32_t is_non_zero = 0;
for (j = 0; j < 8; j++) {
is_non_zero |= k->val[j];
tmp += 0x3fffffff + k->val[j] - (curve->order.val[j] & is_even);
a.val[j] = tmp & 0x3fffffff;
tmp >>= 30;
}
is_non_zero |= k->val[j];
a.val[j] = tmp + 0xffff + k->val[j] - (curve->order.val[j] & is_even);
assert((a.val[0] & 1) != 0);
// special case 0*p: just return zero. We don't care about constant time.
if (!is_non_zero) {
point_set_infinity(res);
return;
}
// Now a = k + 2^256 (mod curve->order) and a is odd.
//
// The idea is to bring the new a into the form.
// sum_{i=0..64} a[i] 16^i, where |a[i]| < 16 and a[i] is odd.
// a[0] is odd, since a is odd. If a[i] would be even, we can
// add 1 to it and subtract 16 from a[i-1]. Afterwards,
// a[64] = 1, which is the 2^256 that we added before.
//
// Since k = a - 2^256 (mod curve->order), we can compute
// k*p = sum_{i=0..63} a[i] 16^i * p
//
// We compute |a[i]| * p in advance for all possible
// values of |a[i]| * p. pmult[i] = (2*i+1) * p
// We compute p, 3*p, ..., 15*p and store it in the table pmult.
// store p^2 temporarily in pmult[7]
pmult[7] = *p;
point_double(curve, &pmult[7]);
// compute 3*p, etc by repeatedly adding p^2.
pmult[0] = *p;
for (i = 1; i < 8; i++) {
pmult[i] = pmult[7];
point_add(curve, &pmult[i-1], &pmult[i]);
}
// now compute res = sum_{i=0..63} a[i] * 16^i * p step by step,
// starting with i = 63.
// initialize jres = |a[63]| * p.
// Note that a[i] = a>>(4*i) & 0xf if (a&0x10) != 0
// and - (16 - (a>>(4*i) & 0xf)) otherwise. We can compute this as
// ((a ^ (((a >> 4) & 1) - 1)) & 0xf) >> 1
// since a is odd.
aptr = &a.val[8];
abits = *aptr;
ashift = 12;
bits = abits >> ashift;
sign = (bits >> 4) - 1;
bits ^= sign;
bits &= 15;
curve_to_jacobian(&pmult[bits>>1], &jres, prime);
for (i = 62; i >= 0; i--) {
// sign = sign(a[i+1]) (0xffffffff for negative, 0 for positive)
// invariant jres = (-1)^sign sum_{j=i+1..63} (a[j] * 16^{j-i-1} * p)
// abits >> (ashift - 4) = lowbits(a >> (i*4))
point_jacobian_double(&jres, curve);
point_jacobian_double(&jres, curve);
point_jacobian_double(&jres, curve);
point_jacobian_double(&jres, curve);
// get lowest 5 bits of a >> (i*4).
ashift -= 4;
if (ashift < 0) {
// the condition only depends on the iteration number and
// leaks no private information to a side-channel.
bits = abits << (-ashift);
abits = *(--aptr);
ashift += 30;
bits |= abits >> ashift;
} else {
bits = abits >> ashift;
}
bits &= 31;
nsign = (bits >> 4) - 1;
bits ^= nsign;
bits &= 15;
// negate last result to make signs of this round and the
// last round equal.
conditional_negate(sign ^ nsign, &jres.z, prime);
// add odd factor
point_jacobian_add(&pmult[bits >> 1], &jres, curve);
sign = nsign;
}
conditional_negate(sign, &jres.z, prime);
jacobian_to_curve(&jres, res, prime);
MEMSET_BZERO(&a, sizeof(a));
MEMSET_BZERO(&jres, sizeof(jres));
}
#if USE_PRECOMPUTED_CP
// res = k * G
// k must be a normalized number with 0 <= k < curve->order
void scalar_multiply(const ecdsa_curve *curve, const bignum256 *k, curve_point *res)
{
assert (bn_is_less(k, &curve->order));
int i, j;
static CONFIDENTIAL bignum256 a;
uint32_t is_even = (k->val[0] & 1) - 1;
uint32_t lowbits;
static CONFIDENTIAL jacobian_curve_point jres;
const bignum256 *prime = &curve->prime;
// is_even = 0xffffffff if k is even, 0 otherwise.
// add 2^256.
// make number odd: subtract curve->order if even
uint32_t tmp = 1;
uint32_t is_non_zero = 0;
for (j = 0; j < 8; j++) {
is_non_zero |= k->val[j];
tmp += 0x3fffffff + k->val[j] - (curve->order.val[j] & is_even);
a.val[j] = tmp & 0x3fffffff;
tmp >>= 30;
}
is_non_zero |= k->val[j];
a.val[j] = tmp + 0xffff + k->val[j] - (curve->order.val[j] & is_even);
assert((a.val[0] & 1) != 0);
// special case 0*G: just return zero. We don't care about constant time.
if (!is_non_zero) {
point_set_infinity(res);
return;
}
// Now a = k + 2^256 (mod curve->order) and a is odd.
//
// The idea is to bring the new a into the form.
// sum_{i=0..64} a[i] 16^i, where |a[i]| < 16 and a[i] is odd.
// a[0] is odd, since a is odd. If a[i] would be even, we can
// add 1 to it and subtract 16 from a[i-1]. Afterwards,
// a[64] = 1, which is the 2^256 that we added before.
//
// Since k = a - 2^256 (mod curve->order), we can compute
// k*G = sum_{i=0..63} a[i] 16^i * G
//
// We have a big table curve->cp that stores all possible
// values of |a[i]| 16^i * G.
// curve->cp[i][j] = (2*j+1) * 16^i * G
// now compute res = sum_{i=0..63} a[i] * 16^i * G step by step.
// initial res = |a[0]| * G. Note that a[0] = a & 0xf if (a&0x10) != 0
// and - (16 - (a & 0xf)) otherwise. We can compute this as
// ((a ^ (((a >> 4) & 1) - 1)) & 0xf) >> 1
// since a is odd.
lowbits = a.val[0] & ((1 << 5) - 1);
lowbits ^= (lowbits >> 4) - 1;
lowbits &= 15;
curve_to_jacobian(&curve->cp[0][lowbits >> 1], &jres, prime);
for (i = 1; i < 64; i ++) {
// invariant res = sign(a[i-1]) sum_{j=0..i-1} (a[j] * 16^j * G)
// shift a by 4 places.
for (j = 0; j < 8; j++) {
a.val[j] = (a.val[j] >> 4) | ((a.val[j + 1] & 0xf) << 26);
}
a.val[j] >>= 4;
// a = old(a)>>(4*i)
// a is even iff sign(a[i-1]) = -1
lowbits = a.val[0] & ((1 << 5) - 1);
lowbits ^= (lowbits >> 4) - 1;
lowbits &= 15;
// negate last result to make signs of this round and the
// last round equal.
conditional_negate((lowbits & 1) - 1, &jres.y, prime);
// add odd factor
point_jacobian_add(&curve->cp[i][lowbits >> 1], &jres, curve);
}
conditional_negate(((a.val[0] >> 4) & 1) - 1, &jres.y, prime);
jacobian_to_curve(&jres, res, prime);
MEMSET_BZERO(&a, sizeof(a));
MEMSET_BZERO(&jres, sizeof(jres));
}
#else
void scalar_multiply(const ecdsa_curve *curve, const bignum256 *k, curve_point *res)
{
point_multiply(curve, k, &curve->G, res);
}
#endif
int ecdh_multiply(const ecdsa_curve *curve, const uint8_t *priv_key, const uint8_t *pub_key, uint8_t *session_key)
{
curve_point point;
if (!ecdsa_read_pubkey(curve, pub_key, &point)) {
return 1;
}
bignum256 k;
bn_read_be(priv_key, &k);
point_multiply(curve, &k, &point, &point);
MEMSET_BZERO(&k, sizeof(k));
session_key[0] = 0x04;
bn_write_be(&point.x, session_key + 1);
bn_write_be(&point.y, session_key + 33);
MEMSET_BZERO(&point, sizeof(point));
return 0;
}
void init_rfc6979(const uint8_t *priv_key, const uint8_t *hash, rfc6979_state *state) {
uint8_t bx[2*32];
uint8_t buf[32 + 1 + 2*32];
memcpy(bx, priv_key, 32);
memcpy(bx+32, hash, 32);
memset(state->v, 1, sizeof(state->v));
memset(state->k, 0, sizeof(state->k));
memcpy(buf, state->v, sizeof(state->v));
buf[sizeof(state->v)] = 0x00;
memcpy(buf + sizeof(state->v) + 1, bx, 64);
hmac_sha256(state->k, sizeof(state->k), buf, sizeof(buf), state->k);
hmac_sha256(state->k, sizeof(state->k), state->v, sizeof(state->v), state->v);
memcpy(buf, state->v, sizeof(state->v));
buf[sizeof(state->v)] = 0x01;
memcpy(buf + sizeof(state->v) + 1, bx, 64);
hmac_sha256(state->k, sizeof(state->k), buf, sizeof(buf), state->k);
hmac_sha256(state->k, sizeof(state->k), state->v, sizeof(state->v), state->v);
MEMSET_BZERO(bx, sizeof(bx));
MEMSET_BZERO(buf, sizeof(buf));
}
// generate next number from deterministic random number generator
void generate_rfc6979(uint8_t rnd[32], rfc6979_state *state)
{
uint8_t buf[32 + 1];
hmac_sha256(state->k, sizeof(state->k), state->v, sizeof(state->v), state->v);
memcpy(buf, state->v, sizeof(state->v));
buf[sizeof(state->v)] = 0x00;
hmac_sha256(state->k, sizeof(state->k), buf, sizeof(state->v) + 1, state->k);
hmac_sha256(state->k, sizeof(state->k), state->v, sizeof(state->v), state->v);
memcpy(rnd, buf, 32);
MEMSET_BZERO(buf, sizeof(buf));
}
// generate K in a deterministic way, according to RFC6979
// http://tools.ietf.org/html/rfc6979
void generate_k_rfc6979(bignum256 *k, rfc6979_state *state)
{
uint8_t buf[32];
generate_rfc6979(buf, state);
bn_read_be(buf, k);
MEMSET_BZERO(buf, sizeof(buf));
}
// msg is a data to be signed
// msg_len is the message length
int ecdsa_sign(const ecdsa_curve *curve, const uint8_t *priv_key, const uint8_t *msg, uint32_t msg_len, uint8_t *sig, uint8_t *pby, int (*is_canonical)(uint8_t by, uint8_t sig[64]))
{
uint8_t hash[32];
sha256_Raw(msg, msg_len, hash);
int res = ecdsa_sign_digest(curve, priv_key, hash, sig, pby, is_canonical);
MEMSET_BZERO(hash, sizeof(hash));
return res;
}
// msg is a data to be signed
// msg_len is the message length
int ecdsa_sign_double(const ecdsa_curve *curve, const uint8_t *priv_key, const uint8_t *msg, uint32_t msg_len, uint8_t *sig, uint8_t *pby, int (*is_canonical)(uint8_t by, uint8_t sig[64]))
{
uint8_t hash[32];
sha256_Raw(msg, msg_len, hash);
sha256_Raw(hash, 32, hash);
int res = ecdsa_sign_digest(curve, priv_key, hash, sig, pby, is_canonical);
MEMSET_BZERO(hash, sizeof(hash));
return res;
}
// uses secp256k1 curve
// priv_key is a 32 byte big endian stored number
// sig is 64 bytes long array for the signature
// digest is 32 bytes of digest
// is_canonical is an optional function that checks if the signature
// conforms to additional coin-specific rules.
int ecdsa_sign_digest(const ecdsa_curve *curve, const uint8_t *priv_key, const uint8_t *digest, uint8_t *sig, uint8_t *pby, int (*is_canonical)(uint8_t by, uint8_t sig[64]))
{
int i;
curve_point R;
bignum256 k, z, randk;
bignum256 *s = &R.y;
uint8_t by; // signature recovery byte
#if USE_RFC6979
rfc6979_state rng;
init_rfc6979(priv_key, digest, &rng);
#endif
bn_read_be(digest, &z);
for (i = 0; i < 10000; i++) {
#if USE_RFC6979
// generate K deterministically
generate_k_rfc6979(&k, &rng);
// if k is too big or too small, we don't like it
if (bn_is_zero(&k) || !bn_is_less(&k, &curve->order)) {
continue;
}
#else
// generate random number k
generate_k_random(&k, &curve->order);
#endif
// compute k*G
scalar_multiply(curve, &k, &R);
by = R.y.val[0] & 1;
// r = (rx mod n)
if (!bn_is_less(&R.x, &curve->order)) {
bn_subtract(&R.x, &curve->order, &R.x);
by |= 2;
}
// if r is zero, we retry
if (bn_is_zero(&R.x)) {
continue;
}
// randomize operations to counter side-channel attacks
generate_k_random(&randk, &curve->order);
bn_multiply(&randk, &k, &curve->order); // k*rand
bn_inverse(&k, &curve->order); // (k*rand)^-1
bn_read_be(priv_key, s); // priv
bn_multiply(&R.x, s, &curve->order); // R.x*priv
bn_add(s, &z); // R.x*priv + z
bn_multiply(&k, s, &curve->order); // (k*rand)^-1 (R.x*priv + z)
bn_multiply(&randk, s, &curve->order); // k^-1 (R.x*priv + z)
bn_mod(s, &curve->order);
// if s is zero, we retry
if (bn_is_zero(s)) {
continue;
}
// if S > order/2 => S = -S
if (bn_is_less(&curve->order_half, s)) {
bn_subtract(&curve->order, s, s);
by ^= 1;
}
// we are done, R.x and s is the result signature
bn_write_be(&R.x, sig);
bn_write_be(s, sig + 32);
// check if the signature is acceptable or retry
if (is_canonical && !is_canonical(by, sig)) {
continue;
}
if (pby) {
*pby = by;
}
MEMSET_BZERO(&k, sizeof(k));
MEMSET_BZERO(&randk, sizeof(randk));
#if USE_RFC6979
MEMSET_BZERO(&rng, sizeof(rng));
#endif
return 0;
}
// Too many retries without a valid signature
// -> fail with an error
MEMSET_BZERO(&k, sizeof(k));
MEMSET_BZERO(&randk, sizeof(randk));
#if USE_RFC6979
MEMSET_BZERO(&rng, sizeof(rng));
#endif
return -1;
}
void ecdsa_get_public_key33(const ecdsa_curve *curve, const uint8_t *priv_key, uint8_t *pub_key)
{
curve_point R;
bignum256 k;
bn_read_be(priv_key, &k);
// compute k*G
scalar_multiply(curve, &k, &R);
pub_key[0] = 0x02 | (R.y.val[0] & 0x01);
bn_write_be(&R.x, pub_key + 1);
MEMSET_BZERO(&R, sizeof(R));
MEMSET_BZERO(&k, sizeof(k));
}
void ecdsa_get_public_key65(const ecdsa_curve *curve, const uint8_t *priv_key, uint8_t *pub_key)
{
curve_point R;
bignum256 k;
bn_read_be(priv_key, &k);
// compute k*G
scalar_multiply(curve, &k, &R);
pub_key[0] = 0x04;
bn_write_be(&R.x, pub_key + 1);
bn_write_be(&R.y, pub_key + 33);
MEMSET_BZERO(&R, sizeof(R));
MEMSET_BZERO(&k, sizeof(k));
}
int ecdsa_uncompress_pubkey(const ecdsa_curve *curve, const uint8_t *pub_key, uint8_t *uncompressed)
{
curve_point pub;
if (!ecdsa_read_pubkey(curve, pub_key, &pub)) {
return 0;
}
uncompressed[0] = 4;
bn_write_be(&pub.x, uncompressed + 1);
bn_write_be(&pub.y, uncompressed + 33);
return 1;
}
void ecdsa_get_pubkeyhash(const uint8_t *pub_key, uint8_t *pubkeyhash)
{
uint8_t h[32];
if (pub_key[0] == 0x04) { // uncompressed format
sha256_Raw(pub_key, 65, h);
} else if (pub_key[0] == 0x00) { // point at infinity
sha256_Raw(pub_key, 1, h);
} else {
sha256_Raw(pub_key, 33, h); // expecting compressed format
}
ripemd160(h, 32, pubkeyhash);
MEMSET_BZERO(h, sizeof(h));
}
void ecdsa_get_address_raw(const uint8_t *pub_key, uint32_t version, uint8_t *addr_raw)
{
size_t prefix_len = address_prefix_bytes_len(version);
address_write_prefix_bytes(version, addr_raw);
ecdsa_get_pubkeyhash(pub_key, addr_raw + prefix_len);
}
void ecdsa_get_address(const uint8_t *pub_key, uint32_t version, char *addr, int addrsize)
{
uint8_t raw[MAX_ADDR_RAW_SIZE];
size_t prefix_len = address_prefix_bytes_len(version);
ecdsa_get_address_raw(pub_key, version, raw);
base58_encode_check(raw, 20 + prefix_len, addr, addrsize);
// not as important to clear this one, but we might as well
MEMSET_BZERO(raw, sizeof(raw));
}
void ecdsa_get_address_segwit_p2sh_raw(const uint8_t *pub_key, uint32_t version, uint8_t *addr_raw)
{
size_t prefix_len = address_prefix_bytes_len(version);
uint8_t digest[32];
addr_raw[0] = 0; // version byte
addr_raw[1] = 20; // push 20 bytes
ecdsa_get_pubkeyhash(pub_key, addr_raw + 2);
sha256_Raw(addr_raw, 22, digest);
address_write_prefix_bytes(version, addr_raw);
ripemd160(digest, 32, addr_raw + prefix_len);
}
void ecdsa_get_address_segwit_p2sh(const uint8_t *pub_key, uint32_t version, char *addr, int addrsize)
{
uint8_t raw[MAX_ADDR_RAW_SIZE];
size_t prefix_len = address_prefix_bytes_len(version);
ecdsa_get_address_segwit_p2sh_raw(pub_key, version, raw);
base58_encode_check(raw, prefix_len + 20, addr, addrsize);
MEMSET_BZERO(raw, sizeof(raw));
}
void ecdsa_get_wif(const uint8_t *priv_key, uint32_t version, char *wif, int wifsize)
{
uint8_t wif_raw[MAX_WIF_RAW_SIZE];
size_t prefix_len = address_prefix_bytes_len(version);
address_write_prefix_bytes(version, wif_raw);
memcpy(wif_raw + prefix_len, priv_key, 32);
wif_raw[prefix_len + 32] = 0x01;
base58_encode_check(wif_raw, prefix_len + 32 + 1, wif, wifsize);
// private keys running around our stack can cause trouble
MEMSET_BZERO(wif_raw, sizeof(wif_raw));
}
int ecdsa_address_decode(const char *addr, uint32_t version, uint8_t *out)
{
if (!addr) return 0;
int prefix_len = address_prefix_bytes_len(version);
return base58_decode_check(addr, out, 20 + prefix_len) == 20 + prefix_len
&& address_check_prefix(out, version);
}
void uncompress_coords(const ecdsa_curve *curve, uint8_t odd, const bignum256 *x, bignum256 *y)
{
// y^2 = x^3 + a*x + b
memcpy(y, x, sizeof(bignum256)); // y is x
bn_multiply(x, y, &curve->prime); // y is x^2
bn_subi(y, -curve->a, &curve->prime); // y is x^2 + a
bn_multiply(x, y, &curve->prime); // y is x^3 + ax
bn_add(y, &curve->b); // y is x^3 + ax + b
bn_sqrt(y, &curve->prime); // y = sqrt(y)
if ((odd & 0x01) != (y->val[0] & 1)) {
bn_subtract(&curve->prime, y, y); // y = -y
}
}
int ecdsa_read_pubkey(const ecdsa_curve *curve, const uint8_t *pub_key, curve_point *pub)
{
if (!curve) {
curve = &secp256k1;
}
if (pub_key[0] == 0x04) {
bn_read_be(pub_key + 1, &(pub->x));
bn_read_be(pub_key + 33, &(pub->y));
return ecdsa_validate_pubkey(curve, pub);
}
if (pub_key[0] == 0x02 || pub_key[0] == 0x03) { // compute missing y coords
bn_read_be(pub_key + 1, &(pub->x));
uncompress_coords(curve, pub_key[0], &(pub->x), &(pub->y));
return ecdsa_validate_pubkey(curve, pub);
}
// error
return 0;
}
// Verifies that:
// - pub is not the point at infinity.
// - pub->x and pub->y are in range [0,p-1].
// - pub is on the curve.
int ecdsa_validate_pubkey(const ecdsa_curve *curve, const curve_point *pub)
{
bignum256 y_2, x3_ax_b;
if (point_is_infinity(pub)) {
return 0;
}
if (!bn_is_less(&(pub->x), &curve->prime) || !bn_is_less(&(pub->y), &curve->prime)) {
return 0;
}
memcpy(&y_2, &(pub->y), sizeof(bignum256));
memcpy(&x3_ax_b, &(pub->x), sizeof(bignum256));
// y^2
bn_multiply(&(pub->y), &y_2, &curve->prime);
bn_mod(&y_2, &curve->prime);
// x^3 + ax + b
bn_multiply(&(pub->x), &x3_ax_b, &curve->prime); // x^2
bn_subi(&x3_ax_b, -curve->a, &curve->prime); // x^2 + a
bn_multiply(&(pub->x), &x3_ax_b, &curve->prime); // x^3 + ax
bn_addmod(&x3_ax_b, &curve->b, &curve->prime); // x^3 + ax + b
bn_mod(&x3_ax_b, &curve->prime);
if (!bn_is_equal(&x3_ax_b, &y_2)) {
return 0;
}
return 1;
}
// uses secp256k1 curve
// pub_key - 65 bytes uncompressed key
// signature - 64 bytes signature
// msg is a data that was signed
// msg_len is the message length
int ecdsa_verify(const ecdsa_curve *curve, const uint8_t *pub_key, const uint8_t *sig, const uint8_t *msg, uint32_t msg_len)
{
uint8_t hash[32];
sha256_Raw(msg, msg_len, hash);
int res = ecdsa_verify_digest(curve, pub_key, sig, hash);
MEMSET_BZERO(hash, sizeof(hash));
return res;
}
int ecdsa_verify_double(const ecdsa_curve *curve, const uint8_t *pub_key, const uint8_t *sig, const uint8_t *msg, uint32_t msg_len)
{
uint8_t hash[32];
sha256_Raw(msg, msg_len, hash);
sha256_Raw(hash, 32, hash);
int res = ecdsa_verify_digest(curve, pub_key, sig, hash);
MEMSET_BZERO(hash, sizeof(hash));
return res;
}
// Compute public key from signature and recovery id.
// returns 0 if verification succeeded
int ecdsa_verify_digest_recover(const ecdsa_curve *curve, uint8_t *pub_key, const uint8_t *sig, const uint8_t *digest, int recid)
{
bignum256 r, s, e;
curve_point cp, cp2;
// read r and s
bn_read_be(sig, &r);
bn_read_be(sig + 32, &s);
if (!bn_is_less(&r, &curve->order) || bn_is_zero(&r)) {
return 1;
}
if (!bn_is_less(&s, &curve->order) || bn_is_zero(&s)) {
return 1;
}
// cp = R = k * G (k is secret nonce when signing)
memcpy(&cp.x, &r, sizeof(bignum256));
if (recid & 2) {
bn_add(&cp.x, &curve->order);
if (!bn_is_less(&cp.x, &curve->prime)) {
return 1;
}
}
// compute y from x
uncompress_coords(curve, recid & 1, &cp.x, &cp.y);
if (!ecdsa_validate_pubkey(curve, &cp)) {
return 1;
}
// e = -digest
bn_read_be(digest, &e);
bn_subtractmod(&curve->order, &e, &e, &curve->order);
bn_fast_mod(&e, &curve->order);
bn_mod(&e, &curve->order);
// r := r^-1
bn_inverse(&r, &curve->order);
// cp := s * R = s * k *G
point_multiply(curve, &s, &cp, &cp);
// cp2 := -digest * G
scalar_multiply(curve, &e, &cp2);
// cp := (s * k - digest) * G = (r*priv) * G = r * Pub
point_add(curve, &cp2, &cp);
// cp := r^{-1} * r * Pub = Pub
point_multiply(curve, &r, &cp, &cp);
pub_key[0] = 0x04;
bn_write_be(&cp.x, pub_key + 1);
bn_write_be(&cp.y, pub_key + 33);
return 0;
}
// returns 0 if verification succeeded
int ecdsa_verify_digest(const ecdsa_curve *curve, const uint8_t *pub_key, const uint8_t *sig, const uint8_t *digest)
{
curve_point pub, res;
bignum256 r, s, z;
if (!ecdsa_read_pubkey(curve, pub_key, &pub)) {
return 1;
}
bn_read_be(sig, &r);
bn_read_be(sig + 32, &s);
bn_read_be(digest, &z);
if (bn_is_zero(&r) || bn_is_zero(&s) ||
(!bn_is_less(&r, &curve->order)) ||
(!bn_is_less(&s, &curve->order))) return 2;
bn_inverse(&s, &curve->order); // s^-1
bn_multiply(&s, &z, &curve->order); // z*s^-1
bn_mod(&z, &curve->order);
bn_multiply(&r, &s, &curve->order); // r*s^-1
bn_mod(&s, &curve->order);
int result = 0;
if (bn_is_zero(&z)) {
// our message hashes to zero
// I don't expect this to happen any time soon
result = 3;
} else {
scalar_multiply(curve, &z, &res);
}
if (result == 0) {
// both pub and res can be infinity, can have y = 0 OR can be equal -> false negative
point_multiply(curve, &s, &pub, &pub);
point_add(curve, &pub, &res);
bn_mod(&(res.x), &curve->order);
// signature does not match
if (!bn_is_equal(&res.x, &r)) {
result = 5;
}
}
MEMSET_BZERO(&pub, sizeof(pub));
MEMSET_BZERO(&res, sizeof(res));
MEMSET_BZERO(&r, sizeof(r));
MEMSET_BZERO(&s, sizeof(s));
MEMSET_BZERO(&z, sizeof(z));
// all OK
return result;
}
int ecdsa_sig_to_der(const uint8_t *sig, uint8_t *der)
{
int i;
uint8_t *p = der, *len, *len1, *len2;
*p = 0x30; p++; // sequence
*p = 0x00; len = p; p++; // len(sequence)
*p = 0x02; p++; // integer
*p = 0x00; len1 = p; p++; // len(integer)
// process R
i = 0;
while (sig[i] == 0 && i < 32) { i++; } // skip leading zeroes
if (sig[i] >= 0x80) { // put zero in output if MSB set
*p = 0x00; p++; *len1 = *len1 + 1;
}
while (i < 32) { // copy bytes to output
*p = sig[i]; p++; *len1 = *len1 + 1; i++;
}
*p = 0x02; p++; // integer
*p = 0x00; len2 = p; p++; // len(integer)
// process S
i = 32;
while (sig[i] == 0 && i < 64) { i++; } // skip leading zeroes
if (sig[i] >= 0x80) { // put zero in output if MSB set
*p = 0x00; p++; *len2 = *len2 + 1;
}
while (i < 64) { // copy bytes to output
*p = sig[i]; p++; *len2 = *len2 + 1; i++;
}
*len = *len1 + *len2 + 4;
return *len + 2;
}
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